Dissipative particle dynamics simulations are employed to study surfactant-mediated forces between a pair of perpendicular carbon nanotubes (CNTs) coated by surfcatants which form spherical micelles in bulk solution and on the tubes. Two force regimes are observed: at small tube/tube distances the force is attractive, whereas it is repulsive at larger distances. The attractive regime is dominated by a central micelle binding the tubes, while in the repulsive regime the contact region is depleted. The two regimes are separated by a discontinuous transition. The repulsive regime is critical for stabilizing CNT suspensions. Viewing rebundling as a thermally activated process, a connection between the repulsive force and the rebundling rate is established. We find that a larger hydrophilic surfactant headgroup creates a stronger and longer ranged tube/tube force, which reduces the rebundling rate significantly. The longer range originates directly from the further reaching head corona of the adsorbed surfactant layer. The larger magnitude of the force appears to be related to the axial compression force the adsorbed phase can sustain. This compression force appears to be the most critical factor for suspension design.